College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises: 19

Answer

(a) $t=\frac{\ln\frac{10}{3}}{12\ln\frac{41}{40}}$ (b) $t\approx 4.063202$

Work Step by Step

(a) We need to solve: $300(1.025)^{12t}=1000$ $(1.025)^{12t}=\frac{1000}{300}$ $(\frac{41}{40})^{12t}=\frac{10}{3}$ We take the natural log of both sides and use log rules to simplify: $12t\ln\frac{41}{40}=\ln\frac{10}{3}$ $12t=\frac{\ln\frac{10}{3}}{\ln\frac{41}{40}}$ $t=\frac{\ln\frac{10}{3}}{12\ln\frac{41}{40}}$ (b) We solve using a calculator: $t\approx 4.063202$
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